Writing a number in exponential form through prime factorization

Express the following numbers as a product of powers of prime factors:

(i) 72

Thus, 72 = 2 × 3 (required prime factor product form)

(ii)Find the remaining numbers as a product of powers of prime factors (ii) 432 (iii) 1000 (iv) 16000

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Let's solve this example in another way:

1000 = 10 × 100 = 10 × 10 × 10

= (2 × 5) × (2 × 5) × (2 × 5) (Since 10 = 2 × 5)

= 2 × 5 × 2 × 5 × 2 × 5 = 2 × 2 × 2 × 5 × 5 × 5

or 1000 = 2 × 5

Is this method correct?

Work out 15, −13, −14, −103, −54.

(i) 15 = 1 × 1 × 1 × 1 × 1 =

In fact, you will realise that 1 raised to any power is 1.

(ii) −13 = (–1) × (–1) × (–1) = 1 × (–1) =

(iii) −14 = (–1) × (–1) × (–1) × (–1) = 1 ×1 =

You may check that (–1) raised to any odd power is (–1),and (–1) raised to any even power is (+1).

(iv) −103 = (–10) × (–10) × (–10) = 100 × (–10) =

(v) −54 = (–5) × (–5) × (–5) × (–5) = 25 × 25 =

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